|
| |
|
|
A124668
|
|
Numbers that together with their prime factors contain every digit exactly once.
|
|
2
|
| |
|
|
|
OFFSET
|
1,1
|
|
|
COMMENTS
|
The exponents in the prime factorization are not considered here. See A273260 for that variant, which contains, e.g., 26487 = 3^5 * 109 and 61054 = 2 * 7^3 * 89. - M. F. Hasler, May 28 2024
|
|
|
LINKS
|
|
|
|
EXAMPLE
|
10968 = 2^3 * 3 * 457.
|
|
|
MAPLE
|
isA124668 := proc(n) local digs, digs2, f, fac, b ; digs := convert(n, base, 10) ; f := ifactors(n)[2] ; for fac from 1 to nops(f) do b := op(1, op(fac, f)) ; digs := [op(digs), op(convert(b, base, 10))] ; od ; digs2 := convert(digs, set) ; if nops(digs2) = 10 and nops(digs2)=nops(digs) then print(n, f) ; RETURN(true) ; else RETURN(false) ; fi ; end : A124668aux := proc(n, dleft) local i, nnxt, dnxt ; isA124668(n) : for i from 1 to nops(dleft) do nnxt := 10*n+op(i, dleft) ; dnxt := dleft minus {op(i, dleft)} ; if nops(dnxt) > 0 then A124668aux(nnxt, dnxt) ; fi ; od ; end : dleft := {0, 1, 2, 3, 4, 5, 6, 7, 8, 9} : for i from 1 to 9 do dnxt := dleft minus {i} ; A124668aux(i, dnxt) : od : # R. J. Mathar, Jan 13 2007
|
|
|
MATHEMATICA
|
Select[Range[2, 1000000], Sort[Join[IntegerDigits[ # ], Flatten[IntegerDigits[Transpose[FactorInteger[ # ]][[1]]]]]] == {0, 1, 2, 3, 4, 5, 6, 7, 8, 9} &]
|
|
|
PROG
|
(PARI) is_A124668(n) = { vecsum([logint(f, 10)+1 | f<-n=concat(factor(n)[, 1], n)])==10 && #Set(concat([digits(f) | f<-n]))>9 }
L=List(); forvec(v=vector(5, i, [0, 9]), forperm(v, n, is_A124668(n=fromdigits(Vec(n)))&& listput(L, n)), 2); A124668=Set(L) \\ M. F. Hasler, Jun 05 2024
|
|
|
CROSSREFS
|
Cf. A273260: similar, but digits of exponents > 1 in the prime factorization are also taken into account.
|
|
|
KEYWORD
|
base,fini,full,nonn
|
|
|
AUTHOR
|
|
|
|
STATUS
|
approved
|
| |
|
|
